LMFDB - Embedded newform 972.2.l.b.215.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,-3,0,3,-6,0,0,9,0,-3,0,0,6,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			215.15
Character	$\chi$	$=$	972.215
Dual form			972.2.l.b.755.15

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37930 + 0.312303i) q^{2} +(1.80493 + 0.861519i) q^{4} +(1.46028 - 1.74029i) q^{5} +(0.448132 - 1.23123i) q^{7} +(2.22049 + 1.75198i) q^{8} +(2.55766 - 1.94434i) q^{10} +(2.07176 - 1.73841i) q^{11} +(0.789120 - 4.47532i) q^{13} +(1.00263 - 1.55829i) q^{14} +(2.51557 + 3.10997i) q^{16} +(-4.20783 - 2.42939i) q^{17} +(-5.44971 + 3.14639i) q^{19} +(4.13500 - 1.88306i) q^{20} +(3.40048 - 1.75077i) q^{22} +(-2.38405 + 0.867725i) q^{23} +(-0.0279630 - 0.158586i) q^{25} +(2.48609 - 5.92636i) q^{26} +(1.86958 - 1.83622i) q^{28} +(4.85038 - 0.855253i) q^{29} +(0.999738 + 2.74676i) q^{31} +(2.49847 + 5.07520i) q^{32} +(-5.04515 - 4.66498i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(-8.49941 + 2.63785i) q^{38} +(6.29149 - 1.30592i) q^{40} +(3.91196 + 0.689785i) q^{41} +(-5.46733 - 6.51571i) q^{43} +(5.23705 - 1.35286i) q^{44} +(-3.55932 + 0.452305i) q^{46} +(11.2519 + 4.09536i) q^{47} +(4.04720 + 3.39600i) q^{49} +(0.0109576 - 0.227471i) q^{50} +(5.27988 - 7.39781i) q^{52} +3.84281i q^{53} -6.14402i q^{55} +(3.15217 - 1.94882i) q^{56} +(6.95722 + 0.335138i) q^{58} +(8.77893 + 7.36639i) q^{59} +(-0.0369509 - 0.0134490i) q^{61} +(0.521117 + 4.10082i) q^{62} +(1.86114 + 7.78050i) q^{64} +(-6.63603 - 7.90851i) q^{65} +(-11.7530 - 2.07238i) q^{67} +(-5.50189 - 8.01001i) q^{68} +(-1.24776 - 4.02040i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-7.41349 + 8.01766i) q^{74} +(-12.5470 + 0.984001i) q^{76} +(-1.21197 - 3.32985i) q^{77} +(-5.93205 + 1.04598i) q^{79} +(9.08569 + 0.163591i) q^{80} +(5.18035 + 2.17314i) q^{82} +(-1.65768 - 9.40119i) q^{83} +(-10.3725 + 3.77526i) q^{85} +(-5.50621 - 10.6946i) q^{86} +(7.64596 - 0.230448i) q^{88} +(5.99050 - 3.45862i) q^{89} +(-5.15653 - 2.97713i) q^{91} +(-5.05062 - 0.487722i) q^{92} +(14.2408 + 9.16274i) q^{94} +(-2.48245 + 14.0787i) q^{95} +(-6.70720 + 5.62801i) q^{97} +(4.52172 + 5.94806i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.37930	+	0.312303i	0.975312	+	0.220832i
$2$	1.37930	+	0.312303i	0.975312	+	0.220832i
$3$		0			0
$3$		0			0
$4$	1.80493	+	0.861519i	0.902467	+	0.430759i
$5$	1.46028	−	1.74029i	0.653057	−	0.778282i	−0.333315	−	0.942816i	$-0.608167\pi$
$5$	1.46028	−	1.74029i	0.653057	−	0.778282i	0.986372	+	0.164533i	$0.0526117\pi$
$6$		0			0
$7$	0.448132	−	1.23123i	0.169378	−	0.465363i	−0.825740	−	0.564050i	$-0.809242\pi$
$7$	0.448132	−	1.23123i	0.169378	−	0.465363i	0.995118	+	0.0986879i	$0.0314646\pi$
$8$	2.22049	+	1.75198i	0.785061	+	0.619418i
$9$		0			0
$10$	2.55766	−	1.94434i	0.808803	−	0.614853i
$11$	2.07176	−	1.73841i	0.624658	−	0.524150i	−0.274606	−	0.961557i	$-0.588547\pi$
$11$	2.07176	−	1.73841i	0.624658	−	0.524150i	0.899264	+	0.437407i	$0.144103\pi$
$12$		0			0
$13$	0.789120	−	4.47532i	0.218862	−	1.24123i	−0.655215	−	0.755443i	$-0.727422\pi$
$13$	0.789120	−	4.47532i	0.218862	−	1.24123i	0.874077	−	0.485788i	$-0.161467\pi$
$14$	1.00263	−	1.55829i	0.267963	−	0.416470i
$15$		0			0
$16$	2.51557	+	3.10997i	0.628893	+	0.777492i
$17$	−4.20783	−	2.42939i	−1.02055	−	0.589214i	−0.106286	−	0.994336i	$-0.533896\pi$
$17$	−4.20783	−	2.42939i	−1.02055	−	0.589214i	−0.914263	+	0.405122i	$0.867229\pi$
$18$		0			0
$19$	−5.44971	+	3.14639i	−1.25025	+	0.721832i	−0.971159	−	0.238433i	$-0.923366\pi$
$19$	−5.44971	+	3.14639i	−1.25025	+	0.721832i	−0.279090	+	0.960265i	$0.590033\pi$
$20$	4.13500	−	1.88306i	0.924614	−	0.421064i
$21$		0			0
$22$	3.40048	−	1.75077i	0.724985	−	0.373266i
$23$	−2.38405	+	0.867725i	−0.497110	+	0.180933i	−0.578394	−	0.815758i	$-0.696320\pi$
$23$	−2.38405	+	0.867725i	−0.497110	+	0.180933i	0.0812839	+	0.996691i	$0.474098\pi$
$24$		0			0
$25$	−0.0279630	−	0.158586i	−0.00559260	−	0.0317172i
$26$	2.48609	−	5.92636i	0.487562	−	1.16226i
$27$		0			0
$28$	1.86958	−	1.83622i	0.353317	−	0.347013i
$29$	4.85038	−	0.855253i	0.900693	−	0.158816i	0.295918	−	0.955213i	$-0.404374\pi$
$29$	4.85038	−	0.855253i	0.900693	−	0.158816i	0.604775	+	0.796397i	$0.293263\pi$
$30$		0			0
$31$	0.999738	+	2.74676i	0.179558	+	0.493332i	0.996519	−	0.0833604i	$-0.0265653\pi$
$31$	0.999738	+	2.74676i	0.179558	+	0.493332i	−0.816961	+	0.576693i	$0.804343\pi$
$32$	2.49847	+	5.07520i	0.441672	+	0.897177i
$33$		0			0
$34$	−5.04515	−	4.66498i	−0.865236	−	0.800037i
$35$	−1.48831	−	2.57783i	−0.251570	−	0.435732i
$36$		0			0
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	0.351876	+	0.936047i	$0.385544\pi$
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	−0.986578	+	0.163290i	$0.947789\pi$
$38$	−8.49941	+	2.63785i	−1.37879	+	0.427917i
$39$		0			0
$40$	6.29149	−	1.30592i	0.994772	−	0.206485i
$41$	3.91196	+	0.689785i	0.610946	+	0.107726i	0.470556	−	0.882370i	$-0.344053\pi$
$41$	3.91196	+	0.689785i	0.610946	+	0.107726i	0.140390	+	0.990096i	$0.455164\pi$
$42$		0			0
$43$	−5.46733	−	6.51571i	−0.833760	−	0.993637i	−0.999972	−	0.00754644i	$-0.997598\pi$
$43$	−5.46733	−	6.51571i	−0.833760	−	0.993637i	0.166211	−	0.986090i	$-0.446847\pi$
$44$	5.23705	−	1.35286i	0.789515	−	0.203951i
$45$		0			0
$46$	−3.55932	+	0.452305i	−0.524793	+	0.0666887i
$47$	11.2519	+	4.09536i	1.64126	+	0.597370i	0.987259	−	0.159123i	$-0.0508668\pi$
$47$	11.2519	+	4.09536i	1.64126	+	0.597370i	0.654001	+	0.756493i	$0.273089\pi$
$48$		0			0
$49$	4.04720	+	3.39600i	0.578171	+	0.485143i
$50$	0.0109576	−	0.227471i	0.00154963	−	0.0321692i
$51$		0			0
$52$	5.27988	−	7.39781i	0.732188	−	1.02589i
$53$			3.84281i			0.527851i	0.964543	+	0.263925i	$0.0850173\pi$
$53$			3.84281i			0.527851i	−0.964543	+	0.263925i	$0.914983\pi$
$54$		0			0
$55$		−	6.14402i		−	0.828460i
$56$	3.15217	−	1.94882i	0.421226	−	0.260422i
$57$		0			0
$58$	6.95722	+	0.335138i	0.913528	+	0.0440058i
$59$	8.77893	+	7.36639i	1.14292	+	0.959023i	0.999530	−	0.0306438i	$-0.00975574\pi$
$59$	8.77893	+	7.36639i	1.14292	+	0.959023i	0.143388	+	0.989666i	$0.454200\pi$
$60$		0			0
$61$	−0.0369509	−	0.0134490i	−0.00473108	−	0.00172197i	0.339654	−	0.940551i	$-0.389690\pi$
$61$	−0.0369509	−	0.0134490i	−0.00473108	−	0.00172197i	−0.344385	+	0.938829i	$0.611912\pi$
$62$	0.521117	+	4.10082i	0.0661820	+	0.520805i
$63$		0			0
$64$	1.86114	+	7.78050i	0.232643	+	0.972562i
$65$	−6.63603	−	7.90851i	−0.823098	−	0.980930i
$66$		0			0
$67$	−11.7530	−	2.07238i	−1.43586	−	0.253181i	−0.599068	−	0.800698i	$-0.704462\pi$
$67$	−11.7530	−	2.07238i	−1.43586	−	0.253181i	−0.836795	+	0.547517i	$0.815573\pi$
$68$	−5.50189	−	8.01001i	−0.667202	−	0.971357i
$69$		0			0
$70$	−1.24776	−	4.02040i	−0.149136	−	0.480529i
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	−0.929546	−	0.368707i	$-0.879801\pi$
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	0.784082	+	0.620657i	$0.213134\pi$
$72$		0			0
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	0.988267	−	0.152734i	$-0.0488077\pi$
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	−0.626405	+	0.779498i	$0.715474\pi$
$74$	−7.41349	+	8.01766i	−0.861801	+	0.932034i
$75$		0			0
$76$	−12.5470	+	0.984001i	−1.43924	+	0.112873i
$77$	−1.21197	−	3.32985i	−0.138116	−	0.379472i
$78$		0			0
$79$	−5.93205	+	1.04598i	−0.667408	+	0.117682i	−0.497079	−	0.867705i	$-0.665594\pi$
$79$	−5.93205	+	1.04598i	−0.667408	+	0.117682i	−0.170329	+	0.985387i	$0.554483\pi$
$80$	9.08569	+	0.163591i	1.01581	+	0.0182900i
$81$		0			0
$82$	5.18035	+	2.17314i	0.572074	+	0.239983i
$83$	−1.65768	−	9.40119i	−0.181954	−	1.03191i	−0.929806	−	0.368049i	$-0.880026\pi$
$83$	−1.65768	−	9.40119i	−0.181954	−	1.03191i	0.747852	−	0.663865i	$-0.231085\pi$
$84$		0			0
$85$	−10.3725	+	3.77526i	−1.12505	+	0.409485i
$86$	−5.50621	−	10.6946i	−0.593750	−	1.15323i
$87$		0			0
$88$	7.64596	−	0.230448i	0.815063	−	0.0245658i
$89$	5.99050	−	3.45862i	0.634991	−	0.366613i	−0.147691	−	0.989034i	$-0.547184\pi$
$89$	5.99050	−	3.45862i	0.634991	−	0.366613i	0.782683	+	0.622421i	$0.213851\pi$
$90$		0			0
$91$	−5.15653	−	2.97713i	−0.540552	−	0.312088i
$92$	−5.05062	−	0.487722i	−0.526564	−	0.0508485i
$93$		0			0
$94$	14.2408	+	9.16274i	1.46882	+	0.945064i
$95$	−2.48245	+	14.0787i	−0.254694	+	1.44444i
$96$		0			0
$97$	−6.70720	+	5.62801i	−0.681012	+	0.571437i	−0.916302	−	0.400488i	$-0.868841\pi$
$97$	−6.70720	+	5.62801i	−0.681012	+	0.571437i	0.235290	+	0.971925i	$0.424396\pi$
$98$	4.52172	+	5.94806i	0.456762	+	0.600844i
$99$		0			0
$100$	0.0861535	−	0.310328i	0.00861535	−	0.0310328i
$101$	−0.753107	+	2.06914i	−0.0749369	+	0.205888i	−0.971505	−	0.237018i	$-0.923830\pi$
$101$	−0.753107	+	2.06914i	−0.0749369	+	0.205888i	0.896568	+	0.442905i	$0.146052\pi$
$102$		0			0
$103$	−1.26442	+	1.50687i	−0.124587	+	0.148476i	−0.824732	−	0.565524i	$-0.808674\pi$
$103$	−1.26442	+	1.50687i	−0.124587	+	0.148476i	0.700145	+	0.714000i	$0.253118\pi$
$104$	9.59289	−	8.55488i	0.940661	−	0.838875i
$105$		0			0
$106$	−1.20012	+	5.30039i	−0.116566	+	0.514819i
$107$	−4.06709			−0.393180			−0.196590	−	0.980486i	$-0.562987\pi$
$107$	−4.06709			−0.393180			−0.196590	+	0.980486i	$0.562987\pi$
$108$		0			0
$109$	−1.81021			−0.173387			−0.0866934	−	0.996235i	$-0.527630\pi$
$109$	−1.81021			−0.173387			−0.0866934	+	0.996235i	$0.527630\pi$
$110$	1.91880	−	8.47445i	0.182950	−	0.808007i
$111$		0			0
$112$	4.95641	−	1.70358i	0.468336	−	0.160973i
$113$	2.25644	−	2.68911i	0.212268	−	0.252971i	−0.649396	−	0.760450i	$-0.724978\pi$
$113$	2.25644	−	2.68911i	0.212268	−	0.252971i	0.861664	+	0.507480i	$0.169423\pi$
$114$		0			0
$115$	−1.97129	+	5.41607i	−0.183824	+	0.505051i
$116$	9.49143	+	2.63502i	0.881257	+	0.244655i
$117$		0			0
$118$	9.80822	+	12.9021i	0.902920	+	1.18774i
$119$	−4.87681	+	4.09213i	−0.447057	+	0.375125i
$120$		0			0
$121$	−0.640026	+	3.62977i	−0.0581842	+	0.329979i
$122$	−0.0467662	−	0.0300901i	−0.00423401	−	0.00272423i
$123$		0			0
$124$	−0.561922	+	5.81901i	−0.0504621	+	0.522562i
$125$	9.52032	+	5.49656i	0.851523	+	0.491627i
$126$		0			0
$127$	−9.71588	+	5.60947i	−0.862145	+	0.497760i	−0.864730	−	0.502237i	$-0.832511\pi$
$127$	−9.71588	+	5.60947i	−0.862145	+	0.497760i	0.00258477	+	0.999997i	$0.499177\pi$
$128$	0.137201	+	11.3129i	0.0121270	+	0.999926i
$129$		0			0
$130$	−6.68322	−	12.9807i	−0.586157	−	1.13848i
$131$	4.82128	−	1.75480i	0.421237	−	0.153318i	−0.122700	−	0.992444i	$-0.539155\pi$
$131$	4.82128	−	1.75480i	0.421237	−	0.153318i	0.543937	+	0.839126i	$0.316933\pi$
$132$		0			0
$133$	1.43175	+	8.11986i	0.124149	+	0.704081i
$134$	−15.5638	−	6.52894i	−1.34450	−	0.564015i
$135$		0			0
$136$	−5.08720	−	12.7665i	−0.436224	−	1.09472i
$137$	−1.78089	+	0.314019i	−0.152152	+	0.0268285i	−0.249205	−	0.968451i	$-0.580169\pi$
$137$	−1.78089	+	0.314019i	−0.152152	+	0.0268285i	0.0970534	+	0.995279i	$0.469058\pi$
$138$		0			0
$139$	−4.44656	−	12.2168i	−0.377152	−	1.03622i	−0.972531	−	0.232772i	$-0.925220\pi$
$139$	−4.44656	−	12.2168i	−0.377152	−	1.03622i	0.595379	−	0.803445i	$-0.297002\pi$
$140$	−0.465453	−	5.93501i	−0.0393379	−	0.501600i
$141$		0			0
$142$	−2.35361	+	2.54542i	−0.197511	+	0.213607i
$143$	−6.14507	−	10.6436i	−0.513877	−	0.890061i
$144$		0			0
$145$	5.59452	−	9.68999i	0.464599	−	0.804710i
$146$	2.59205	+	8.35182i	0.214519	+	0.691201i
$147$		0			0
$148$	−12.7294	+	8.74350i	−1.04635	+	0.718711i
$149$	−2.53451	−	0.446902i	−0.207635	−	0.0366116i	0.0688632	−	0.997626i	$-0.478063\pi$
$149$	−2.53451	−	0.446902i	−0.207635	−	0.0366116i	−0.276498	+	0.961014i	$0.589174\pi$
$150$		0			0
$151$	3.37473	+	4.02185i	0.274632	+	0.327293i	0.885677	−	0.464303i	$-0.153695\pi$
$151$	3.37473	+	4.02185i	0.274632	+	0.327293i	−0.611045	+	0.791596i	$0.709251\pi$
$152$	−17.6134	−	2.56125i	−1.42864	−	0.207744i
$153$		0			0
$154$	−0.631743	−	4.97136i	−0.0509073	−	0.400604i
$155$	6.24006	+	2.27120i	0.501214	+	0.182427i
$156$		0			0
$157$	16.0051	+	13.4298i	1.27734	+	1.07182i	0.993605	+	0.112916i	$0.0360190\pi$
$157$	16.0051	+	13.4298i	1.27734	+	1.07182i	0.283738	+	0.958902i	$0.408425\pi$
$158$	−8.50873	−	0.409877i	−0.676919	−	0.0326080i
$159$		0			0
$160$	12.4808	+	3.06313i	0.986694	+	0.242162i
$161$			3.32418i			0.261982i
$162$		0			0
$163$		−	3.28308i		−	0.257151i	−0.991700	−	0.128575i	$-0.958960\pi$
$163$		−	3.28308i		−	0.257151i	0.991700	−	0.128575i	$-0.0410404\pi$
$164$	6.46657	+	4.61525i	0.504954	+	0.360390i
$165$		0			0
$166$	0.649578	−	13.4848i	0.0504170	−	1.04662i
$167$	−14.6697	−	12.3093i	−1.13517	−	0.952523i	−0.135902	−	0.990722i	$-0.543393\pi$
$167$	−14.6697	−	12.3093i	−1.13517	−	0.952523i	−0.999270	+	0.0381993i	$0.987838\pi$
$168$		0			0
$169$	−7.18977	−	2.61686i	−0.553059	−	0.201297i
$170$	−15.4857	+	1.96787i	−1.18770	+	0.150929i
$171$		0			0
$172$	−4.25476	−	16.4706i	−0.324423	−	1.25587i
$173$	−5.61931	−	6.69683i	−0.427228	−	0.509150i	0.508892	−	0.860830i	$-0.330055\pi$
$173$	−5.61931	−	6.69683i	−0.427228	−	0.509150i	−0.936120	+	0.351680i	$0.885611\pi$
$174$		0			0
$175$	−0.207788	−	0.0366386i	−0.0157073	−	0.00276962i
$176$	10.6180	+	2.07000i	0.800365	+	0.156032i
$177$		0			0
$178$	9.34283	−	2.89962i	0.700274	−	0.217335i
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	−0.730093	−	0.683348i	$-0.760523\pi$
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	0.956843	+	0.290605i	$0.0938565\pi$
$180$		0			0
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	−0.993449	−	0.114276i	$-0.963545\pi$
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	0.397759	−	0.917490i	$-0.369788\pi$
$182$	−6.18264	−	5.71675i	−0.458288	−	0.423754i
$183$		0			0
$184$	−6.81400	−	2.25004i	−0.502335	−	0.165875i
$185$	5.99958	+	16.4837i	0.441098	+	1.21191i
$186$		0			0
$187$	−12.9409	+	2.28182i	−0.946330	+	0.166863i
$188$	16.7807	+	17.0856i	1.22386	+	1.24609i
$189$		0			0
$190$	−7.82087	+	18.6435i	−0.567385	+	1.35254i
$191$	−2.03119	−	11.5195i	−0.146972	−	0.833520i	−0.965763	−	0.259428i	$-0.916466\pi$
$191$	−2.03119	−	11.5195i	−0.146972	−	0.833520i	0.818791	−	0.574092i	$-0.194645\pi$
$192$		0			0
$193$	−16.5117	+	6.00978i	−1.18854	+	0.432593i	−0.859211	−	0.511622i	$-0.829045\pi$
$193$	−16.5117	+	6.00978i	−1.18854	+	0.432593i	−0.329330	+	0.944215i	$0.606823\pi$
$194$	−11.0089	+	5.66803i	−0.790391	+	0.406941i
$195$		0			0
$196$	4.37920	+	9.61630i	0.312800	+	0.686878i
$197$	−19.9607	+	11.5243i	−1.42214	+	0.821074i	−0.996482	−	0.0838089i	$-0.973291\pi$
$197$	−19.9607	+	11.5243i	−1.42214	+	0.821074i	−0.425660	+	0.904883i	$0.639958\pi$
$198$		0			0
$199$	−2.70763	−	1.56325i	−0.191939	−	0.110816i	0.400951	−	0.916099i	$-0.368680\pi$
$199$	−2.70763	−	1.56325i	−0.191939	−	0.110816i	−0.592890	+	0.805284i	$0.702013\pi$
$200$	0.215748	−	0.401129i	0.0152557	−	0.0283641i
$201$		0			0
$202$	−1.68496	+	2.61877i	−0.118553	+	0.184256i
$203$	1.12060	−	6.35522i	0.0786504	−	0.446049i
$204$		0			0
$205$	6.91298	−	5.80068i	0.482824	−	0.405137i
$206$	−2.21461	+	1.68355i	−0.154299	+	0.117298i
$207$		0			0
$208$	15.9032	−	8.80385i	1.10269	−	0.610437i
$209$	−5.82075	+	15.9924i	−0.402630	+	1.10622i
$210$		0			0
$211$	8.26193	−	9.84619i	0.568775	−	0.677839i	−0.402604	−	0.915374i	$-0.631895\pi$
$211$	8.26193	−	9.84619i	0.568775	−	0.677839i	0.971379	+	0.237535i	$0.0763393\pi$
$212$	−3.31065	+	6.93602i	−0.227377	+	0.476368i
$213$		0			0
$214$	−5.60974	−	1.27016i	−0.383474	−	0.0868267i
$215$	−19.3231			−1.31782
$216$		0			0
$217$	3.82992			0.259992
$218$	−2.49682	−	0.565335i	−0.169106	−	0.0382893i
$219$		0			0
$220$	5.29319	−	11.0896i	0.356867	−	0.747657i
$221$	−14.1928	+	16.9143i	−0.954710	+	1.13778i
$222$		0			0
$223$	3.53622	−	9.71568i	0.236803	−	0.650610i	−0.763187	−	0.646177i	$-0.776367\pi$
$223$	3.53622	−	9.71568i	0.236803	−	0.650610i	0.999990	−	0.00443299i	$-0.00141107\pi$
$224$	7.36840	−	0.801844i	0.492322	−	0.0535754i
$225$		0			0
$226$	3.95212	−	3.00440i	0.262891	−	0.199850i
$227$	0.0735740	−	0.0617359i	0.00488328	−	0.00409756i	−0.640343	−	0.768089i	$-0.721208\pi$
$227$	0.0735740	−	0.0617359i	0.00488328	−	0.00409756i	0.645226	+	0.763992i	$0.276763\pi$
$228$		0			0
$229$	4.66642	−	26.4646i	0.308366	−	1.74883i	−0.298856	−	0.954298i	$-0.596605\pi$
$229$	4.66642	−	26.4646i	0.308366	−	1.74883i	0.607222	−	0.794532i	$-0.292284\pi$
$230$	−4.41045	+	6.85475i	−0.290817	+	0.451989i
$231$		0			0
$232$	12.2686	+	6.59868i	0.805473	+	0.433225i
$233$	−6.26494	−	3.61706i	−0.410430	−	0.236962i	0.280545	−	0.959841i	$-0.409485\pi$
$233$	−6.26494	−	3.61706i	−0.410430	−	0.236962i	−0.690974	+	0.722879i	$0.742818\pi$
$234$		0			0
$235$	23.5581	−	13.6013i	1.53676	−	0.887248i
$236$	9.49909	+	20.8591i	0.618338	+	1.35781i
$237$		0			0
$238$	−8.00457	+	4.12123i	−0.518859	+	0.267140i
$239$	−11.9878	+	4.36319i	−0.775424	+	0.282231i	−0.699263	−	0.714864i	$-0.746488\pi$
$239$	−11.9878	+	4.36319i	−0.775424	+	0.282231i	−0.0761609	+	0.997096i	$0.524266\pi$
$240$		0			0
$241$	−1.31501	−	7.45780i	−0.0847073	−	0.480399i	−0.997419	−	0.0717956i	$-0.977127\pi$
$241$	−1.31501	−	7.45780i	−0.0847073	−	0.480399i	0.912712	−	0.408603i	$-0.133984\pi$
$242$	−2.01638	+	4.80666i	−0.129618	+	0.308984i
$243$		0			0
$244$	−0.0551074	−	0.0561085i	−0.00352789	−	0.00359198i
$245$	11.8201	−	2.08420i	0.755157	−	0.133155i
$246$		0			0
$247$	9.78063	+	26.8721i	0.622327	+	1.70983i
$248$	−2.59235	+	7.85067i	−0.164615	+	0.498518i
$249$		0			0
$250$	11.4148	+	10.5546i	0.721934	+	0.667533i
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	0.990411	−	0.138149i	$-0.0441153\pi$
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	−0.614846	+	0.788647i	$0.710782\pi$
$252$		0			0
$253$	−3.43072	+	5.94217i	−0.215687	+	0.373581i
$254$	−15.1530	+	4.70284i	−0.950782	+	0.295082i
$255$		0			0
$256$	−3.34380	+	15.6467i	−0.208988	+	0.977918i
$257$	−5.37613	−	0.947957i	−0.335354	−	0.0591320i	0.00343564	−	0.999994i	$-0.498906\pi$
$257$	−5.37613	−	0.947957i	−0.335354	−	0.0591320i	−0.338790	+	0.940862i	$0.610018\pi$
$258$		0			0
$259$	6.50314	+	7.75014i	0.404086	+	0.481570i
$260$	−5.16426	−	19.9914i	−0.320274	−	1.23981i
$261$		0			0
$262$	7.19802	−	0.914698i	0.444695	−	0.0565102i
$263$	−19.1400	−	6.96640i	−1.18022	−	0.429566i	−0.323943	−	0.946077i	$-0.605009\pi$
$263$	−19.1400	−	6.96640i	−1.18022	−	0.429566i	−0.856281	+	0.516510i	$0.827231\pi$
$264$		0			0
$265$	6.68762	+	5.61158i	0.410817	+	0.344716i
$266$	−0.561044	+	11.6469i	−0.0343998	+	0.714115i
$267$		0			0
$268$	−19.4281	−	13.8660i	−1.18676	−	0.846999i
$269$		−	9.12305i		−	0.556242i	−0.960546	−	0.278121i	$-0.910288\pi$
$269$		−	9.12305i		−	0.556242i	0.960546	−	0.278121i	$-0.0897116\pi$
$270$		0			0
$271$			21.2629i			1.29163i	0.763495	+	0.645813i	$0.223482\pi$
$271$			21.2629i			1.29163i	−0.763495	+	0.645813i	$0.776518\pi$
$272$	−3.02976	−	19.1975i	−0.183706	−	1.16402i
$273$		0			0
$274$	−2.55445	−	0.123051i	−0.154320	−	0.00743379i
$275$	−0.333620	−	0.279940i	−0.0201180	−	0.0168810i
$276$		0			0
$277$	23.9850	+	8.72982i	1.44112	+	0.524524i	0.940096	−	0.340911i	$-0.110735\pi$
$277$	23.9850	+	8.72982i	1.44112	+	0.524524i	0.501022	+	0.865435i	$0.332958\pi$
$278$	−2.31779	−	18.2393i	−0.139012	−	1.09392i
$279$		0			0
$280$	1.21152	−	8.33152i	0.0724023	−	0.497903i
$281$	7.92327	+	9.44259i	0.472663	+	0.563298i	0.948720	−	0.316116i	$-0.102379\pi$
$281$	7.92327	+	9.44259i	0.472663	+	0.563298i	−0.476057	+	0.879414i	$0.657935\pi$
$282$		0			0
$283$	−16.4533	−	2.90116i	−0.978045	−	0.172456i	−0.338296	−	0.941040i	$-0.609851\pi$
$283$	−16.4533	−	2.90116i	−0.978045	−	0.172456i	−0.639749	+	0.768584i	$0.720962\pi$
$284$	−4.04128	+	2.77586i	−0.239806	+	0.164717i
$285$		0			0
$286$	−5.15187	−	16.5998i	−0.304637	−	0.981567i
$287$	2.60236	−	4.50743i	0.153613	−	0.266065i
$288$		0			0
$289$	3.30388	+	5.72249i	0.194346	+	0.336617i
$290$	10.7427	−	11.6182i	0.630835	−	0.682245i
$291$		0			0
$292$	0.966914	+	12.3292i	0.0565843	+	0.721509i
$293$	−4.55894	−	12.5256i	−0.266336	−	0.731752i	−0.998707	−	0.0508459i	$-0.983808\pi$
$293$	−4.55894	−	12.5256i	−0.266336	−	0.731752i	0.732370	−	0.680906i	$-0.238414\pi$
$294$		0			0
$295$	25.6394	−	4.52091i	1.49278	−	0.263218i
$296$	−20.2882	+	8.08448i	−1.17923	+	0.469901i
$297$		0			0
$298$	−3.35627	−	1.40794i	−0.194424	−	0.0815601i
$299$	2.00204	+	11.3541i	0.115781	+	0.656627i
$300$		0			0
$301$	−10.4724	+	3.81166i	−0.603622	+	0.219700i
$302$	3.39873	+	6.60127i	0.195575	+	0.379860i
$303$		0			0
$304$	−23.4943	−	9.03345i	−1.34749	−	0.518104i
$305$	−0.0773639	+	0.0446661i	−0.00442984	+	0.00255757i
$306$		0			0
$307$	18.8505	+	10.8833i	1.07585	+	0.621144i	0.929775	−	0.368129i	$-0.120002\pi$
$307$	18.8505	+	10.8833i	1.07585	+	0.621144i	0.146078	+	0.989273i	$0.453335\pi$
$308$	0.681210	−	7.05429i	0.0388155	−	0.401956i
$309$		0			0
$310$	7.89761	+	5.08145i	0.448554	+	0.288607i
$311$	2.47718	−	14.0488i	0.140468	−	0.796633i	−0.830427	−	0.557128i	$-0.811903\pi$
$311$	2.47718	−	14.0488i	0.140468	−	0.796633i	0.970895	−	0.239506i	$-0.0769854\pi$
$312$		0			0
$313$	16.2981	−	13.6758i	0.921225	−	0.772999i	−0.0529965	−	0.998595i	$-0.516877\pi$
$313$	16.2981	−	13.6758i	0.921225	−	0.772999i	0.974221	+	0.225596i	$0.0724328\pi$
$314$	17.8816	+	23.5222i	1.00912	+	1.32743i
$315$		0			0
$316$	−11.6081	−	3.22265i	−0.653006	−	0.181288i
$317$	2.30546	−	6.33420i	0.129488	−	0.355764i	−0.857959	−	0.513718i	$-0.828268\pi$
$317$	2.30546	−	6.33420i	0.129488	−	0.355764i	0.987446	+	0.157954i	$0.0504898\pi$
$318$		0			0
$319$	8.56202	−	10.2038i	0.479381	−	0.571304i
$320$	16.2581	+	8.12276i	0.908857	+	0.454076i
$321$		0			0
$322$	−1.03815	+	4.58504i	−0.0578540	+	0.255515i
$323$	30.5753			1.70125
$324$		0			0
$325$	−0.731790			−0.0405924
$326$	1.02532	−	4.52835i	0.0567870	−	0.250802i
$327$		0			0
$328$	7.47798	+	8.38533i	0.412903	+	0.463003i
$329$	10.0847	−	12.0185i	0.555987	−	0.662600i
$330$		0			0
$331$	−8.27597	+	22.7380i	−0.454888	+	1.24980i	0.474357	+	0.880333i	$0.342681\pi$
$331$	−8.27597	+	22.7380i	−0.454888	+	1.24980i	−0.929245	+	0.369463i	$0.879542\pi$
$332$	5.10729	−	18.3966i	0.280299	−	1.00965i
$333$		0			0
$334$	−16.3896	−	21.5596i	−0.896800	−	1.17969i
$335$	−20.7693	+	17.4275i	−1.13475	+	0.952165i
$336$		0			0
$337$	3.79458	−	21.5201i	0.206704	−	1.17228i	−0.688032	−	0.725681i	$-0.741525\pi$
$337$	3.79458	−	21.5201i	0.206704	−	1.17228i	0.894736	−	0.446596i	$-0.147364\pi$
$338$	−9.09959	−	5.85483i	−0.494953	−	0.318461i
$339$		0			0
$340$	−21.9741	−	2.12196i	−1.19171	−	0.115079i
$341$	6.84620	+	3.95266i	0.370743	+	0.214048i
$342$		0			0
$343$	13.9379	−	8.04707i	0.752577	−	0.434501i
$344$	−0.724763	−	24.0467i	−0.0390766	−	1.29651i
$345$		0			0
$346$	−5.65927	−	10.9919i	−0.304244	−	0.590926i
$347$	12.1710	−	4.42990i	0.653376	−	0.237809i	0.00600211	−	0.999982i	$-0.498089\pi$
$347$	12.1710	−	4.42990i	0.653376	−	0.237809i	0.647374	+	0.762173i	$0.275867\pi$
$348$		0			0
$349$	−0.671596	−	3.80881i	−0.0359497	−	0.203881i	0.961543	−	0.274656i	$-0.0885639\pi$
$349$	−0.671596	−	3.80881i	−0.0359497	−	0.203881i	−0.997492	+	0.0707748i	$0.977453\pi$
$350$	−0.275159	−	0.115428i	−0.0147079	−	0.00616990i
$351$		0			0
$352$	13.9990	+	6.17120i	0.746149	+	0.328926i
$353$	−2.99642	+	0.528350i	−0.159483	+	0.0281212i	−0.252820	−	0.967513i	$-0.581358\pi$
$353$	−2.99642	+	0.528350i	−0.159483	+	0.0281212i	0.0933363	+	0.995635i	$0.470247\pi$
$354$		0			0
$355$	1.90473	+	5.23319i	0.101092	+	0.277749i
$356$	13.7921	−	1.08165i	0.730981	−	0.0573271i
$357$		0			0
$358$	5.82541	−	6.30015i	0.307882	−	0.332973i
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	0.997438	−	0.0715425i	$-0.0227922\pi$
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	−0.560676	+	0.828035i	$0.689459\pi$
$360$		0			0
$361$	10.2995	−	17.8393i	0.542082	−	0.938913i
$362$	−6.71890	−	21.6489i	−0.353137	−	1.13784i
$363$		0			0
$364$	−6.74235	−	9.81597i	−0.353395	−	0.514496i
$365$	13.8342	+	2.43935i	0.724116	+	0.127681i
$366$		0			0
$367$	−1.41856	−	1.69058i	−0.0740484	−	0.0882474i	0.727748	−	0.685844i	$-0.240567\pi$
$367$	−1.41856	−	1.69058i	−0.0740484	−	0.0882474i	−0.801797	+	0.597597i	$0.796122\pi$
$368$	−8.69586	−	5.23151i	−0.453303	−	0.272711i
$369$		0			0
$370$	3.12731	+	24.6097i	0.162581	+	1.27940i
$371$	4.73140	+	1.72209i	0.245642	+	0.0894064i
$372$		0			0
$373$	−8.03381	−	6.74117i	−0.415975	−	0.349044i	0.410655	−	0.911791i	$-0.365300\pi$
$373$	−8.03381	−	6.74117i	−0.415975	−	0.349044i	−0.826629	+	0.562747i	$0.809745\pi$
$374$	−18.5619	−	0.894153i	−0.959816	−	0.0462356i
$375$		0			0
$376$	17.8098	+	28.8068i	0.918468	+	1.48560i
$377$		−	22.3819i		−	1.15273i
$378$		0			0
$379$			3.08694i			0.158565i	0.996852	+	0.0792826i	$0.0252630\pi$
$379$			3.08694i			0.158565i	−0.996852	+	0.0792826i	$0.974737\pi$
$380$	−16.6097	+	23.2724i	−0.852061	+	1.19385i
$381$		0			0
$382$	0.795942	−	16.5232i	0.0407239	−	0.845398i
$383$	12.3070	+	10.3268i	0.628856	+	0.527673i	0.900573	−	0.434704i	$-0.143147\pi$
$383$	12.3070	+	10.3268i	0.628856	+	0.527673i	−0.271717	+	0.962377i	$0.587592\pi$
$384$		0			0
$385$	−7.56473	−	2.75333i	−0.385534	−	0.140323i
$386$	−24.6515	+	3.13262i	−1.25473	+	0.159446i
$387$		0			0
$388$	−16.9547	+	4.37980i	−0.860743	+	0.222351i
$389$	11.3463	+	13.5220i	0.575280	+	0.685593i	0.972706	−	0.232042i	$-0.0745407\pi$
$389$	11.3463	+	13.5220i	0.575280	+	0.685593i	−0.397425	+	0.917635i	$0.630096\pi$
$390$		0			0
$391$	12.1397	+	2.14056i	0.613933	+	0.108253i
$392$	3.03704	+	14.6314i	0.153393	+	0.738997i
$393$		0			0
$394$	−31.1309	+	9.66170i	−1.56835	+	0.486750i
$395$	−6.84213	+	11.8509i	−0.344265	+	0.596285i
$396$		0			0
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	0.984091	−	0.177663i	$-0.0568538\pi$
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	−0.645907	+	0.763416i	$0.723520\pi$
$398$	−3.24642	−	3.00179i	−0.162728	−	0.150466i
$399$		0			0
$400$	0.422855	−	0.485899i	0.0211427	−	0.0242949i
$401$	−2.31159	−	6.35103i	−0.115435	−	0.317155i	0.868498	−	0.495693i	$-0.165086\pi$
$401$	−2.31159	−	6.35103i	−0.115435	−	0.317155i	−0.983933	+	0.178537i	$0.942863\pi$
$402$		0			0
$403$	13.0815	−	2.30663i	0.651638	−	0.114901i
$404$	−3.14191	+	3.08585i	−0.156316	+	0.153527i
$405$		0			0
$406$	3.53039	−	8.41578i	0.175210	−	0.417668i
$407$	3.62623	+	20.5654i	0.179746	+	1.01939i
$408$		0			0
$409$	−17.7069	+	6.44479i	−0.875551	+	0.318674i	−0.740413	−	0.672152i	$-0.765370\pi$
$409$	−17.7069	+	6.44479i	−0.875551	+	0.318674i	−0.135138	+	0.990827i	$0.543148\pi$
$410$	11.3466	−	5.84193i	0.560371	−	0.288512i
$411$		0			0
$412$	−3.58038	+	1.63049i	−0.176393	+	0.0803283i
$413$	13.0039	−	7.50779i	0.639879	−	0.369434i
$414$		0			0
$415$	−18.7815	−	10.8435i	−0.921947	−	0.532287i
$416$	24.6847	−	7.17653i	1.21027	−	0.351858i
$417$		0			0
$418$	−13.0230	+	20.2404i	−0.636977	+	0.989992i
$419$	3.31570	−	18.8043i	0.161983	−	0.918649i	−0.790139	−	0.612928i	$-0.789991\pi$
$419$	3.31570	−	18.8043i	0.161983	−	0.918649i	0.952121	−	0.305721i	$-0.0988974\pi$
$420$		0			0
$421$	−17.2688	+	14.4903i	−0.841631	+	0.706212i	−0.957930	−	0.287002i	$-0.907341\pi$
$421$	−17.2688	+	14.4903i	−0.841631	+	0.706212i	0.116299	+	0.993214i	$0.462897\pi$
$422$	14.4707	−	11.0006i	0.704421	−	0.535502i
$423$		0			0
$424$	−6.73252	+	8.53292i	−0.326960	+	0.414395i
$425$	−0.267604	+	0.735236i	−0.0129807	+	0.0356642i
$426$		0			0
$427$	−0.0331178	+	0.0394683i	−0.00160268	+	0.00191000i
$428$	−7.34083	−	3.50387i	−0.354832	−	0.169366i
$429$		0			0
$430$	−26.6523	−	6.03465i	−1.28529	−	0.291017i
$431$	10.8059			0.520500			0.260250	−	0.965541i	$-0.416195\pi$
$431$	10.8059			0.520500			0.260250	+	0.965541i	$0.416195\pi$
$432$		0			0
$433$	−37.5914			−1.80653			−0.903264	−	0.429084i	$-0.858836\pi$
$433$	−37.5914			−1.80653			−0.903264	+	0.429084i	$0.858836\pi$
$434$	5.28260	+	1.19609i	0.253573	+	0.0574144i
$435$		0			0
$436$	−3.26731	−	1.55953i	−0.156476	−	0.0746880i
$437$	10.2622	−	12.2300i	0.490908	−	0.585041i
$438$		0			0
$439$	10.9220	−	30.0080i	0.521279	−	1.43220i	−0.347818	−	0.937562i	$-0.613077\pi$
$439$	10.9220	−	30.0080i	0.521279	−	1.43220i	0.869097	−	0.494641i	$-0.164700\pi$
$440$	10.7642	−	13.6427i	0.513163	−	0.650392i
$441$		0			0
$442$	−24.8585	+	18.8974i	−1.18240	+	0.898859i
$443$	28.7890	−	24.1569i	1.36781	−	1.14773i	0.394324	−	0.918972i	$-0.370979\pi$
$443$	28.7890	−	24.1569i	1.36781	−	1.14773i	0.973484	−	0.228755i	$-0.0734655\pi$
$444$		0			0
$445$	2.72879	−	15.4758i	0.129357	−	0.733621i
$446$	7.91174	−	12.2965i	0.374632	−	0.582254i
$447$		0			0
$448$	10.4136	+	1.19519i	0.491999	+	0.0564675i
$449$	6.99926	+	4.04102i	0.330315	+	0.190708i	0.655981	−	0.754777i	$-0.272255\pi$
$449$	6.99926	+	4.04102i	0.330315	+	0.190708i	−0.325666	+	0.945485i	$0.605588\pi$
$450$		0			0
$451$	9.30376	−	5.37153i	0.438097	−	0.252935i
$452$	6.38944	−	2.90971i	0.300534	−	0.136861i
$453$		0			0
$454$	0.120761	−	0.0621750i	0.00566759	−	0.00291802i
$455$	−12.7110	+	4.62644i	−0.595903	+	0.216891i
$456$		0			0
$457$	−0.429633	−	2.43657i	−0.0200974	−	0.113978i	0.973109	−	0.230346i	$-0.0739858\pi$
$457$	−0.429633	−	2.43657i	−0.0200974	−	0.113978i	−0.993206	+	0.116368i	$0.962875\pi$
$458$	14.7014	−	35.0453i	0.686950	−	1.63756i
$459$		0			0
$460$	−8.22409	+	8.07735i	−0.383450	+	0.376608i
$461$	−8.89827	+	1.56901i	−0.414434	+	0.0730759i	−0.376978	−	0.926222i	$-0.623037\pi$
$461$	−8.89827	+	1.56901i	−0.414434	+	0.0730759i	−0.0374563	+	0.999298i	$0.511925\pi$
$462$		0			0
$463$	0.476987	+	1.31051i	0.0221675	+	0.0609046i	0.950283	−	0.311388i	$-0.100794\pi$
$463$	0.476987	+	1.31051i	0.0221675	+	0.0609046i	−0.928115	+	0.372293i	$0.878572\pi$
$464$	14.8613	+	12.9331i	0.689918	+	0.600403i
$465$		0			0
$466$	−7.51161	−	6.94557i	−0.347968	−	0.321747i
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	0.999907	−	0.0136203i	$-0.00433561\pi$
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	−0.511749	+	0.859135i	$0.671002\pi$
$468$		0			0
$469$	−7.81850	+	13.5420i	−0.361025	+	0.625313i
$470$	36.7413	−	11.4029i	1.69475	−	0.525979i
$471$		0			0
$472$	6.58775	+	31.7375i	0.303226	+	1.46084i
$473$	−22.6539	−	3.99450i	−1.04163	−	0.183667i
$474$		0			0
$475$	0.651364	+	0.776265i	0.0298866	+	0.0356175i
$476$	−12.3278	+	3.18456i	−0.565042	+	0.145964i
$477$		0			0
$478$	−17.8974	+	2.27433i	−0.818606	+	0.104025i
$479$	−13.7237	−	4.99501i	−0.627051	−	0.228228i	0.00889607	−	0.999960i	$-0.497168\pi$
$479$	−13.7237	−	4.99501i	−0.627051	−	0.228228i	−0.635947	+	0.771732i	$0.719390\pi$
$480$		0			0
$481$	26.8799	+	22.5549i	1.22562	+	1.02842i
$482$	0.515299	−	10.6972i	0.0234712	−	0.487245i
$483$		0			0
$484$	−4.28232	+	6.00010i	−0.194651	+	0.272732i
$485$			19.8909i			0.903201i
$486$		0			0
$487$			0.282541i			0.0128032i	0.999980	+	0.00640158i	$0.00203770\pi$
$487$			0.282541i			0.0128032i	−0.999980	+	0.00640158i	$0.997962\pi$
$488$	−0.0584867	−	0.0946006i	−0.00264757	−	0.00428237i
$489$		0			0
$490$	16.9543	+	0.816712i	0.765918	+	0.0368953i
$491$	−11.8728	−	9.96249i	−0.535814	−	0.449601i	0.334290	−	0.942470i	$-0.391504\pi$
$491$	−11.8728	−	9.96249i	−0.535814	−	0.449601i	−0.870103	+	0.492869i	$0.835948\pi$
$492$		0			0
$493$	−22.4873	−	8.18471i	−1.01278	−	0.368621i
$494$	5.09819	+	40.1191i	0.229379	+	1.80505i
$495$		0			0
$496$	−6.02742	+	10.0188i	−0.270639	+	0.449858i
$497$	2.06459	+	2.46049i	0.0926097	+	0.110368i
$498$		0			0
$499$	40.2749	+	7.10155i	1.80295	+	0.317909i	0.971384	−	0.237513i	$-0.0763324\pi$
$499$	40.2749	+	7.10155i	1.80295	+	0.317909i	0.831568	+	0.555423i	$0.187443\pi$
$500$	12.4482	+	18.1229i	0.556699	+	0.810479i
$501$		0			0
$502$	4.98839	+	16.0730i	0.222643	+	0.717375i
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	−0.997995	−	0.0632975i	$-0.979838\pi$
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	0.553815	+	0.832640i	$0.313172\pi$
$504$		0			0
$505$	2.50117	+	4.33215i	0.111301	+	0.192778i
$506$	−6.58774	+	7.12462i	−0.292861	+	0.316728i
$507$		0			0
$508$	−22.3692	+	1.75430i	−0.992472	+	0.0778346i
$509$	−9.68384	−	26.6061i	−0.429229	−	1.17930i	−0.946282	−	0.323343i	$-0.895193\pi$
$509$	−9.68384	−	26.6061i	−0.429229	−	1.17930i	0.517053	−	0.855953i	$-0.327029\pi$
$510$		0			0
$511$	7.97886	−	1.40689i	0.352964	−	0.0622371i
$512$	−9.49862	+	20.5372i	−0.419783	+	0.907624i
$513$		0			0
$514$	−7.11925	−	2.98650i	−0.314017	−	0.131729i
$515$	0.775998	+	4.40091i	0.0341946	+	0.193927i
$516$		0			0
$517$	30.4306	−	11.0758i	1.33834	−	0.487115i
$518$	6.54939	+	12.7207i	0.287764	+	0.558916i
$519$		0			0
$520$	−0.879689	−	29.1870i	−0.0385769	−	1.27993i
$521$	18.4642	−	10.6603i	0.808931	−	0.467036i	−0.0376537	−	0.999291i	$-0.511988\pi$
$521$	18.4642	−	10.6603i	0.808931	−	0.467036i	0.846584	+	0.532255i	$0.178655\pi$
$522$		0			0
$523$	17.0213	+	9.82725i	0.744289	+	0.429716i	0.823627	−	0.567132i	$-0.191947\pi$
$523$	17.0213	+	9.82725i	0.744289	+	0.429716i	−0.0793376	+	0.996848i	$0.525281\pi$
$524$	10.2139	+	0.986321i	0.446196	+	0.0430876i
$525$		0			0
$526$	−24.2242	−	15.5862i	−1.05622	−	0.679592i
$527$	2.46622	−	13.9866i	0.107430	−	0.609268i
$528$		0			0
$529$	−12.6883	+	10.6467i	−0.551663	+	0.462900i
$530$	7.47171	+	9.82861i	0.324551	+	0.426927i
$531$		0			0
$532$	−4.41120	+	15.8893i	−0.191250	+	0.688888i
$533$	6.17401	−	16.9630i	0.267426	−	0.734748i
$534$		0			0
$535$	−5.93909	+	7.07793i	−0.256769	+	0.306005i
$536$	−22.4667	−	25.1928i	−0.970415	−	1.08816i
$537$		0			0
$538$	2.84916	−	12.5834i	0.122836	−	0.542510i
$539$	14.2884			0.615447
$540$		0			0
$541$	41.1619			1.76969			0.884844	−	0.465888i	$-0.154265\pi$
$541$	41.1619			1.76969			0.884844	+	0.465888i	$0.154265\pi$
$542$	−6.64046	+	29.3279i	−0.285232	+	1.25974i
$543$		0			0
$544$	1.81649	−	27.4253i	0.0778814	−	1.17585i
$545$	−2.64341	+	3.15030i	−0.113231	+	0.134944i
$546$		0			0
$547$	−2.48445	+	6.82596i	−0.106227	+	0.291857i	−0.981406	−	0.191942i	$-0.938521\pi$
$547$	−2.48445	+	6.82596i	−0.106227	+	0.291857i	0.875179	+	0.483799i	$0.160744\pi$
$548$	−3.48492	−	0.967487i	−0.148869	−	0.0413290i
$549$		0			0
$550$	−0.372736	−	0.490312i	−0.0158935	−	0.0209070i
$551$	−23.7422	+	19.9221i	−1.01145	+	0.848709i
$552$		0			0
$553$	−1.37050	+	7.77247i	−0.0582795	+	0.330519i
$554$	30.3561	+	19.5316i	1.28971	+	0.829819i
$555$		0			0
$556$	2.49927	−	25.8813i	0.105993	−	1.09761i
$557$	−32.2123	−	18.5978i	−1.36488	−	0.788012i	−0.374609	−	0.927183i	$-0.622223\pi$
$557$	−32.2123	−	18.5978i	−1.36488	−	0.788012i	−0.990268	+	0.139170i	$0.955556\pi$
$558$		0			0
$559$	−33.4743	+	19.3264i	−1.41581	+	0.817419i
$560$	4.27301	−	11.1133i	0.180568	−	0.469622i
$561$		0			0
$562$	7.97962	+	15.4986i	0.336600	+	0.653770i
$563$	41.7085	−	15.1806i	1.75780	−	0.639788i	0.757881	−	0.652392i	$-0.226235\pi$
$563$	41.7085	−	15.1806i	1.75780	−	0.639788i	0.999921	+	0.0126049i	$0.00401237\pi$
$564$		0			0
$565$	−1.38482	−	7.85371i	−0.0582599	−	0.330408i
$566$	−21.7879	−	9.13997i	−0.915816	−	0.384181i
$567$		0			0
$568$	−6.44104	+	2.56663i	−0.270260	+	0.107694i
$569$	−29.0449	+	5.12140i	−1.21763	+	0.214700i	−0.745303	−	0.666726i	$-0.767695\pi$
$569$	−29.0449	+	5.12140i	−1.21763	+	0.214700i	−0.472322	+	0.881426i	$0.656584\pi$
$570$		0			0
$571$	4.48049	+	12.3101i	0.187503	+	0.515160i	0.997452	−	0.0713402i	$-0.0227276\pi$
$571$	4.48049	+	12.3101i	0.187503	+	0.515160i	−0.809949	+	0.586500i	$0.800505\pi$
$572$	−1.92181	−	24.5050i	−0.0803548	−	1.02461i
$573$		0			0
$574$	4.99712	−	5.40436i	0.208576	−	0.225574i
$575$	0.204274	+	0.353814i	0.00851883	+	0.0147550i
$576$		0			0
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	−0.820881	−	0.571099i	$-0.806517\pi$
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	0.905027	+	0.425355i	$0.139851\pi$
$578$	2.76989	+	8.92484i	0.115212	+	0.371225i
$579$		0			0
$580$	18.4458	−	12.6700i	0.765922	−	0.526093i
$581$	−12.3179	−	2.17198i	−0.511033	−	0.0901090i
$582$		0			0
$583$	6.68038	+	7.96137i	0.276673	+	0.329726i
$584$	−2.51677	+	17.3076i	−0.104145	+	0.716192i
$585$		0			0
$586$	−2.37637	−	18.7003i	−0.0981667	−	0.772502i
$587$	−6.83715	−	2.48852i	−0.282199	−	0.102712i	0.197043	−	0.980395i	$-0.436866\pi$
$587$	−6.83715	−	2.48852i	−0.282199	−	0.102712i	−0.479242	+	0.877683i	$0.659088\pi$
$588$		0			0
$589$	−14.0907	−	11.8235i	−0.580595	−	0.487177i
$590$	36.7762	+	1.77156i	1.51405	+	0.0729339i
$591$		0			0
$592$	−30.5084	+	4.81485i	−1.25389	+	0.197889i
$593$			2.93118i			0.120369i	0.998187	+	0.0601846i	$0.0191689\pi$
$593$			2.93118i			0.120369i	−0.998187	+	0.0601846i	$0.980831\pi$
$594$		0			0
$595$			14.4627i			0.592914i
$596$	−4.18960	−	2.99015i	−0.171613	−	0.122481i
$597$		0			0
$598$	−0.784518	+	16.2860i	−0.0320813	+	0.665984i
$599$	−1.03995	−	0.872619i	−0.0424911	−	0.0356543i	0.621295	−	0.783577i	$-0.286607\pi$
$599$	−1.03995	−	0.872619i	−0.0424911	−	0.0356543i	−0.663786	+	0.747923i	$0.731051\pi$
$600$		0			0
$601$	−7.27189	−	2.64675i	−0.296626	−	0.107963i	0.189420	−	0.981896i	$-0.439339\pi$
$601$	−7.27189	−	2.64675i	−0.296626	−	0.107963i	−0.486047	+	0.873933i	$0.661561\pi$
$602$	−15.6350	+	1.98684i	−0.637236	+	0.0809777i
$603$		0			0
$604$	2.62627	+	10.1666i	0.106861	+	0.413672i
$605$	5.38225	+	6.41431i	0.218819	+	0.260779i
$606$		0			0
$607$	11.2517	+	1.98398i	0.456692	+	0.0805271i	0.397262	−	0.917705i	$-0.369961\pi$
$607$	11.2517	+	1.98398i	0.456692	+	0.0805271i	0.0594302	+	0.998232i	$0.481072\pi$
$608$	−29.5845	−	19.7972i	−1.19981	−	0.802881i
$609$		0			0
$610$	−0.120657	+	0.0374469i	−0.00488527	+	0.00151618i
$611$	27.2072	−	47.1242i	1.10068	−	1.90644i
$612$		0			0
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	0.514137	−	0.857708i	$-0.328112\pi$
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	−0.999865	+	0.0164015i	$0.994779\pi$
$614$	22.6015	+	20.8984i	0.912124	+	0.843391i
$615$		0			0
$616$	3.14267	−	9.51724i	0.126622	−	0.383460i
$617$	16.5026	+	45.3406i	0.664371	+	1.82534i	0.555909	+	0.831243i	$0.312370\pi$
$617$	16.5026	+	45.3406i	0.664371	+	1.82534i	0.108462	+	0.994101i	$0.465407\pi$
$618$		0			0
$619$	−4.44121	+	0.783104i	−0.178507	+	0.0314756i	−0.262187	−	0.965017i	$-0.584444\pi$
$619$	−4.44121	+	0.783104i	−0.178507	+	0.0314756i	0.0836800	+	0.996493i	$0.473333\pi$
$620$	9.30621	+	9.47528i	0.373747	+	0.380537i
$621$		0			0
$622$	7.80425	−	18.6038i	0.312922	−	0.745946i
$623$	−1.57383	−	8.92562i	−0.0630541	−	0.357597i
$624$		0			0
$625$	24.2246	−	8.81702i	0.968982	−	0.352681i
$626$	26.7510	−	13.7730i	1.06918	−	0.550480i
$627$		0			0
$628$	17.3180	+	38.0286i	0.691064	+	1.51751i
$629$	32.4907	−	18.7585i	1.29549	−	0.747951i
$630$		0			0
$631$	−9.73065	−	5.61799i	−0.387371	−	0.223649i	0.293649	−	0.955913i	$-0.405130\pi$
$631$	−9.73065	−	5.61799i	−0.387371	−	0.223649i	−0.681020	+	0.732264i	$0.738464\pi$
$632$	−15.0046	−	8.07023i	−0.596850	−	0.321017i
$633$		0			0
$634$	5.15811	−	8.01676i	0.204855	−	0.318386i
$635$	−4.42578	+	25.0999i	−0.175632	+	0.996058i
$636$		0			0
$637$	18.3919	−	15.4327i	0.728714	−	0.611464i
$638$	14.9963	−	11.4002i	0.593708	−	0.451337i
$639$		0			0
$640$	19.8881	+	16.2812i	0.786145	+	0.643570i
$641$	13.8530	−	38.0609i	0.547163	−	1.50332i	−0.290362	−	0.956917i	$-0.593776\pi$
$641$	13.8530	−	38.0609i	0.547163	−	1.50332i	0.837524	−	0.546400i	$-0.184002\pi$
$642$		0			0
$643$	20.7380	−	24.7146i	0.817827	−	0.974648i	−0.182136	−	0.983273i	$-0.558301\pi$
$643$	20.7380	−	24.7146i	0.817827	−	0.974648i	0.999963	+	0.00862524i	$0.00274553\pi$
$644$	−2.86385	+	5.99993i	−0.112851	+	0.236430i
$645$		0			0
$646$	42.1724	+	9.54874i	1.65925	+	0.375690i
$647$	−7.00490			−0.275391			−0.137696	−	0.990475i	$-0.543970\pi$
$647$	−7.00490			−0.275391			−0.137696	+	0.990475i	$0.543970\pi$
$648$		0			0
$649$	30.9936			1.21660
$650$	−1.00936	−	0.228540i	−0.0395902	−	0.00896408i
$651$		0			0
$652$	2.82844	−	5.92575i	0.110770	−	0.232070i
$653$	−22.5667	+	26.8939i	−0.883102	+	1.05244i	0.115150	+	0.993348i	$0.463265\pi$
$653$	−22.5667	+	26.8939i	−0.883102	+	1.05244i	−0.998253	+	0.0590921i	$0.981179\pi$
$654$		0			0
$655$	3.98654	−	10.9529i	0.155767	−	0.427967i
$656$	7.69561	+	13.9013i	0.300463	+	0.542754i
$657$		0			0
$658$	17.6632	−	13.4276i	0.688584	−	0.523462i
$659$	6.86177	−	5.75771i	0.267297	−	0.224289i	−0.499281	−	0.866440i	$-0.666402\pi$
$659$	6.86177	−	5.75771i	0.267297	−	0.224289i	0.766578	+	0.642152i	$0.221958\pi$
$660$		0			0
$661$	−6.18560	+	35.0803i	−0.240592	+	1.36447i	0.589919	+	0.807463i	$0.299160\pi$
$661$	−6.18560	+	35.0803i	−0.240592	+	1.36447i	−0.830511	+	0.557003i	$0.811951\pi$
$662$	−18.5162	+	28.7779i	−0.719652	+	1.11849i
$663$		0			0
$664$	12.7898	−	23.7795i	0.496341	−	0.922822i
$665$	16.2217	+	9.36560i	0.629050	+	0.363182i
$666$		0			0
$667$	−10.8214	+	6.24776i	−0.419008	+	0.241914i
$668$	−15.8731	−	34.8557i	−0.614147	−	1.34861i
$669$		0			0
$670$	−34.0897	+	17.5514i	−1.31700	+	0.678070i
$671$	−0.0999332	+	0.0363727i	−0.00385788	+	0.00140415i
$672$		0			0
$673$	−0.586335	−	3.32527i	−0.0226015	−	0.128180i	0.971419	−	0.237370i	$-0.0762854\pi$
$673$	−0.586335	−	3.32527i	−0.0226015	−	0.128180i	−0.994021	+	0.109190i	$0.965174\pi$
$674$	11.9547	−	28.4977i	0.460477	−	1.09769i
$675$		0			0
$676$	−10.7226	−	10.9174i	−0.412407	−	0.419900i
$677$	1.13808	−	0.200675i	0.0437401	−	0.00771256i	−0.151735	−	0.988421i	$-0.548486\pi$
$677$	1.13808	−	0.200675i	0.0437401	−	0.00771256i	0.195475	+	0.980709i	$0.437375\pi$
$678$		0			0
$679$	3.92368	+	10.7802i	0.150577	+	0.413707i
$680$	−29.6461	−	9.78938i	−1.13688	−	0.375406i
$681$		0			0
$682$	8.20853	+	7.58998i	0.314321	+	0.290636i
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	−0.901070	−	0.433673i	$-0.857217\pi$
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	0.0749630	−	0.997186i	$-0.476116\pi$
$684$		0			0
$685$	−2.05411	+	3.55783i	−0.0784836	+	0.135938i
$686$	21.7377	−	6.74646i	0.829949	−	0.257581i
$687$		0			0
$688$	6.51019	−	33.3940i	0.248199	−	1.27313i
$689$	17.1978	+	3.03244i	0.655184	+	0.115527i
$690$		0			0
$691$	8.25397	+	9.83670i	0.313996	+	0.374206i	0.899842	−	0.436217i	$-0.143682\pi$
$691$	8.25397	+	9.83670i	0.313996	+	0.374206i	−0.585846	+	0.810423i	$0.699238\pi$
$692$	−4.37303	−	16.9285i	−0.166238	−	0.643524i
$693$		0			0
$694$	18.1710	−	2.30910i	0.689761	−	0.0876523i
$695$	−27.7540	−	10.1016i	−1.05277	−	0.383177i
$696$		0			0
$697$	−14.7851	−	12.4062i	−0.560026	−	0.469918i
$698$	0.263171	−	5.46323i	0.00996117	−	0.206786i
$699$		0			0
$700$	−0.343478	−	0.245143i	−0.0129823	−	0.00926554i
$701$		−	3.10248i		−	0.117179i	−0.998282	−	0.0585896i	$-0.981340\pi$
$701$		−	3.10248i		−	0.117179i	0.998282	−	0.0585896i	$-0.0186603\pi$
$702$		0			0
$703$		−	48.5896i		−	1.83259i
$704$	17.3815	+	12.8839i	0.655091	+	0.485579i
$705$		0			0
$706$	−4.29797	−	0.207039i	−0.161756	−	0.00779200i
$707$	2.21011	+	1.85450i	0.0831197	+	0.0697457i
$708$		0			0
$709$	−9.07129	−	3.30168i	−0.340680	−	0.123997i	0.166014	−	0.986123i	$-0.446910\pi$
$709$	−9.07129	−	3.30168i	−0.340680	−	0.123997i	−0.506694	+	0.862126i	$0.669132\pi$
$710$	0.992846	+	7.81299i	0.0372609	+	0.293216i
$711$		0			0
$712$	19.3613	+	2.81540i	0.725594	+	0.105512i
$713$	−4.76686	−	5.68092i	−0.178520	−	0.212752i
$714$		0			0
$715$	−27.4965	−	4.84837i	−1.02831	−	0.181319i
$716$	10.0025	−	6.87050i	0.373812	−	0.256763i
$717$		0			0
$718$	6.93792	+	22.3546i	0.258921	+	0.834267i
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	0.151711	+	0.988425i	$0.451522\pi$
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	−0.931856	+	0.362827i	$0.881812\pi$
$720$		0			0
$721$	1.28869	+	2.23207i	0.0479931	+	0.0831266i
$722$	19.7774	−	21.3892i	0.736040	−	0.796024i
$723$		0			0
$724$	−2.50635	−	31.9586i	−0.0931479	−	1.18773i
$725$	−0.271262	−	0.745287i	−0.0100744	−	0.0276793i
$726$		0			0
$727$	0.483085	−	0.0851808i	0.0179166	−	0.00315918i	−0.164683	−	0.986347i	$-0.552660\pi$
$727$	0.483085	−	0.0851808i	0.0179166	−	0.00315918i	0.182599	+	0.983187i	$0.441549\pi$
$728$	−6.23417	−	15.6448i	−0.231054	−	0.579835i
$729$		0			0
$730$	18.3197	+	7.68506i	0.678043	+	0.284437i
$731$	7.17638	+	40.6993i	0.265428	+	1.50532i
$732$		0			0
$733$	−27.5380	+	10.0230i	−1.01714	+	0.370208i	−0.796170	−	0.605073i	$-0.793144\pi$
$733$	−27.5380	+	10.0230i	−1.01714	+	0.370208i	−0.220969	+	0.975281i	$0.570922\pi$
$734$	−1.42865	−	2.77483i	−0.0527325	−	0.102421i
$735$		0			0
$736$	−10.3604	−	9.93156i	−0.381888	−	0.366082i
$737$	−27.9521	+	16.1381i	−1.02963	+	0.594456i
$738$		0			0
$739$	34.8536	+	20.1228i	1.28211	+	0.740227i	0.977234	−	0.212164i	$-0.0680512\pi$
$739$	34.8536	+	20.1228i	1.28211	+	0.740227i	0.304877	+	0.952392i	$0.401384\pi$
$740$	−3.37218	+	34.9208i	−0.123964	+	1.28371i
$741$		0			0
$742$	5.98820	+	3.85291i	0.219834	+	0.141445i
$743$	−6.83166	+	38.7443i	−0.250629	+	1.42139i	0.556418	+	0.830902i	$0.312175\pi$
$743$	−6.83166	+	38.7443i	−0.250629	+	1.42139i	−0.807047	+	0.590487i	$0.798936\pi$
$744$		0			0
$745$	−4.47882	+	3.75818i	−0.164091	+	0.137689i
$746$	−8.97574	−	11.8071i	−0.328625	−	0.432287i
$747$		0			0
$748$	−25.3232	−	7.03026i	−0.925909	−	0.257052i
$749$	−1.82259	+	5.00754i	−0.0665962	+	0.182971i
$750$		0			0
$751$	−17.6268	+	21.0068i	−0.643211	+	0.766549i	−0.984874	−	0.173273i	$-0.944566\pi$
$751$	−17.6268	+	21.0068i	−0.643211	+	0.766549i	0.341663	+	0.939823i	$0.389010\pi$
$752$	15.5685	+	45.2953i	0.567726	+	1.65175i
$753$		0			0
$754$	6.98993	−	30.8713i	0.254558	−	1.12427i
$755$	11.9272			0.434077
$756$		0			0
$757$	−13.2822			−0.482750			−0.241375	−	0.970432i	$-0.577598\pi$
$757$	−13.2822			−0.482750			−0.241375	+	0.970432i	$0.577598\pi$
$758$	−0.964059	+	4.25781i	−0.0350162	+	0.154651i
$759$		0			0
$760$	−30.1778	+	26.9124i	−1.09466	+	0.976215i
$761$	8.27376	−	9.86029i	0.299924	−	0.357435i	−0.594944	−	0.803767i	$-0.702826\pi$
$761$	8.27376	−	9.86029i	0.299924	−	0.357435i	0.894867	+	0.446332i	$0.147270\pi$
$762$		0			0
$763$	−0.811214	+	2.22879i	−0.0293679	+	0.0806877i
$764$	6.25807	−	22.5418i	0.226409	−	0.815534i
$765$		0			0
$766$	13.7499	+	18.0872i	0.496804	+	0.653517i
$767$	39.8946	−	33.4755i	1.44051	−	1.20873i
$768$		0			0
$769$	5.04800	−	28.6286i	0.182036	−	1.03237i	−0.747670	−	0.664071i	$-0.768827\pi$
$769$	5.04800	−	28.6286i	0.182036	−	1.03237i	0.929705	−	0.368304i	$-0.120061\pi$
$770$	−9.57415	−	6.16016i	−0.345028	−	0.221997i
$771$		0			0
$772$	−34.9801	−	3.37791i	−1.25896	−	0.121574i
$773$	−4.16046	−	2.40204i	−0.149641	−	0.0863954i	0.423310	−	0.905985i	$-0.360868\pi$
$773$	−4.16046	−	2.40204i	−0.149641	−	0.0863954i	−0.572951	+	0.819590i	$0.694202\pi$
$774$		0			0
$775$	0.407642	−	0.235352i	0.0146429	−	0.00845410i
$776$	−24.7534	+	0.746062i	−0.888595	+	0.0267821i
$777$		0			0
$778$	11.4270	+	22.1944i	0.409677	+	0.795707i
$779$	−23.4894	+	8.54944i	−0.841595	+	0.306315i
$780$		0			0
$781$	1.15124	+	6.52903i	0.0411948	+	0.233627i
$782$	16.0758	+	6.74375i	0.574870	+	0.241156i
$783$		0			0
$784$	−0.380445	+	21.1295i	−0.0135873	+	0.754626i
$785$	46.7437	−	8.24217i	1.66835	−	0.294176i
$786$		0			0
$787$	−13.7229	−	37.7035i	−0.489170	−	1.34398i	−0.901433	−	0.432919i	$-0.857484\pi$
$787$	−13.7229	−	37.7035i	−0.489170	−	1.34398i	0.412263	−	0.911065i	$-0.364739\pi$
$788$	−45.9562	+	3.60411i	−1.63712	+	0.128391i
$789$		0			0
$790$	−13.1384	+	14.2092i	−0.467444	+	0.505539i
$791$	−2.29975	−	3.98328i	−0.0817696	−	0.141629i
$792$		0			0
$793$	−0.0893474	+	0.154754i	−0.00317282	+	0.00549548i
$794$	5.64921	+	18.2023i	0.200483	+	0.645974i
$795$		0			0
$796$	−3.54032	−	5.15424i	−0.125483	−	0.182687i
$797$	30.6136	+	5.39800i	1.08439	+	0.191207i	0.687156	−	0.726510i	$-0.258859\pi$
$797$	30.6136	+	5.39800i	1.08439	+	0.191207i	0.397234	+	0.917717i	$0.369970\pi$
$798$		0			0
$799$	−37.3969	−	44.5679i	−1.32301	−	1.57670i
$800$	0.734991	−	0.538141i	0.0259859	−	0.0190262i
$801$		0			0
$802$	−1.20492	−	9.48189i	−0.0425473	−	0.334817i
$803$	15.7147	+	5.71967i	0.554559	+	0.201843i
$804$		0			0
$805$	5.78505	+	4.85423i	0.203896	+	0.171089i
$806$	18.7637	+	0.903872i	0.660924	+	0.0318375i
$807$		0			0
$808$	−5.29736	+	3.27508i	−0.186361	+	0.115217i
$809$			26.7938i			0.942021i	0.882128	+	0.471010i	$0.156111\pi$
$809$			26.7938i			0.942021i	−0.882128	+	0.471010i	$0.843889\pi$
$810$		0			0
$811$		−	22.6335i		−	0.794769i	−0.917652	−	0.397384i	$-0.869918\pi$
$811$		−	22.6335i		−	0.794769i	0.917652	−	0.397384i	$-0.130082\pi$
$812$	7.49774	−	10.5053i	0.263119	−	0.368665i
$813$		0			0
$814$	−1.42097	+	29.4983i	−0.0498050	+	1.03392i
$815$	−5.71352	−	4.79422i	−0.200136	−	0.167934i
$816$		0			0
$817$	50.2963	+	18.3064i	1.75965	+	0.640459i
$818$	−26.4359	+	3.35937i	−0.924309	+	0.117458i
$819$		0			0
$820$	17.4749	−	4.51418i	0.610249	−	0.157642i
$821$	−8.22523	−	9.80244i	−0.287062	−	0.342108i	0.603171	−	0.797612i	$-0.293903\pi$
$821$	−8.22523	−	9.80244i	−0.287062	−	0.342108i	−0.890234	+	0.455504i	$0.849459\pi$
$822$		0			0
$823$	−25.5687	−	4.50845i	−0.891269	−	0.157155i	−0.290782	−	0.956789i	$-0.593915\pi$
$823$	−25.5687	−	4.50845i	−0.891269	−	0.157155i	−0.600487	+	0.799635i	$0.705027\pi$
$824$	−5.44763	+	1.13076i	−0.189777	+	0.0393920i
$825$		0			0
$826$	20.2809	−	6.29434i	0.705664	−	0.219008i
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	−0.646866	−	0.762603i	$-0.723921\pi$
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	0.983867	+	0.178901i	$0.0572542\pi$
$828$		0			0
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	−0.999223	−	0.0394143i	$-0.987451\pi$
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	0.465478	−	0.885060i	$-0.345883\pi$
$830$	−22.5188	−	20.8220i	−0.781641	−	0.722741i
$831$		0			0
$832$	36.2889	−	2.18947i	1.25809	−	0.0759062i
$833$	−8.77970	−	24.1220i	−0.304199	−	0.835779i
$834$		0			0
$835$	−42.8436	+	7.55448i	−1.48266	+	0.261434i
$836$	−24.2838	+	23.8505i	−0.839872	+	0.824886i
$837$		0			0
$838$	10.4460	−	24.9012i	0.360850	−	0.860199i
$839$	1.89878	+	10.7685i	0.0655533	+	0.371771i	0.999882	+	0.0153587i	$0.00488902\pi$
$839$	1.89878	+	10.7685i	0.0655533	+	0.371771i	−0.934329	+	0.356412i	$0.884000\pi$
$840$		0			0
$841$	−4.45636	+	1.62198i	−0.153668	+	0.0559304i
$842$	−28.3442	+	14.5933i	−0.976807	+	0.502919i
$843$		0			0
$844$	23.3949	−	10.6539i	0.805286	−	0.366723i
$845$	−15.0532	+	8.69096i	−0.517845	+	0.298978i
$846$		0			0
$847$	4.18228	+	2.41464i	0.143705	+	0.0829680i
$848$	−11.9510	+	9.66687i	−0.410400	+	0.331962i
$849$		0			0
$850$	−0.598723	+	0.930537i	−0.0205360	+	0.0319172i
$851$	3.40174	−	19.2923i	0.116610	−	0.661330i
$852$		0			0
$853$	4.92621	−	4.13359i	0.168670	−	0.141531i	−0.554545	−	0.832154i	$-0.687108\pi$
$853$	4.92621	−	4.13359i	0.168670	−	0.141531i	0.723216	+	0.690622i	$0.242663\pi$
$854$	−0.0580054	+	0.0440958i	−0.00198490	+	0.00150893i
$855$		0			0
$856$	−9.03093	−	7.12545i	−0.308671	−	0.243543i
$857$	1.08582	−	2.98327i	0.0370910	−	0.101907i	−0.919765	−	0.392470i	$-0.871621\pi$
$857$	1.08582	−	2.98327i	0.0370910	−	0.101907i	0.956856	+	0.290564i	$0.0938428\pi$
$858$		0			0
$859$	−18.2176	+	21.7108i	−0.621575	+	0.740765i	−0.981340	−	0.192278i	$-0.938412\pi$
$859$	−18.2176	+	21.7108i	−0.621575	+	0.740765i	0.359765	+	0.933043i	$0.382857\pi$
$860$	−34.8769	−	16.6472i	−1.18929	−	0.567664i
$861$		0			0
$862$	14.9045	+	3.37470i	0.507649	+	0.114943i
$863$	−53.5310			−1.82222			−0.911108	−	0.412168i	$-0.864772\pi$
$863$	−53.5310			−1.82222			−0.911108	+	0.412168i	$0.864772\pi$
$864$		0			0
$865$	−19.8602			−0.675267
$866$	−51.8498	−	11.7399i	−1.76193	−	0.398939i
$867$		0			0
$868$	6.91274	+	3.29954i	0.234634	+	0.111994i
$869$	−10.4714	+	12.4793i	−0.355218	+	0.423333i
$870$		0			0
$871$	−18.5491	+	50.9633i	−0.628513	+	1.72682i
$872$	−4.01956	−	3.17145i	−0.136119	−	0.107399i
$873$		0			0
$874$	17.9741	−	13.6639i	0.607984	−	0.462190i
$875$	11.0339	−	9.25855i	0.373014	−	0.312996i
$876$		0			0
$877$	−5.19031	+	29.4357i	−0.175264	+	0.993974i	0.762574	+	0.646901i	$0.223935\pi$
$877$	−5.19031	+	29.4357i	−0.175264	+	0.993974i	−0.937838	+	0.347073i	$0.887176\pi$
$878$	24.4363	−	37.9790i	0.824686	−	1.28173i
$879$		0			0
$880$	19.1077	−	15.4557i	0.644121	−	0.521012i
$881$	−14.9002	−	8.60262i	−0.502000	−	0.289830i	0.227539	−	0.973769i	$-0.426932\pi$
$881$	−14.9002	−	8.60262i	−0.502000	−	0.289830i	−0.729539	+	0.683939i	$0.760265\pi$
$882$		0			0
$883$	19.9228	−	11.5024i	0.670455	−	0.387088i	−0.125794	−	0.992056i	$-0.540148\pi$
$883$	19.9228	−	11.5024i	0.670455	−	0.387088i	0.796249	+	0.604969i	$0.206814\pi$
$884$	−40.1890	+	18.3018i	−1.35170	+	0.615558i
$885$		0			0
$886$	47.2529	−	24.3286i	1.58749	−	0.817337i
$887$	−26.8201	+	9.76172i	−0.900531	+	0.327767i	−0.750466	−	0.660909i	$-0.770171\pi$
$887$	−26.8201	+	9.76172i	−0.900531	+	0.327767i	−0.150066	+	0.988676i	$0.547948\pi$
$888$		0			0
$889$	2.55256	+	14.4763i	0.0856102	+	0.485520i
$890$	8.59695	−	20.4935i	0.288170	−	0.686944i
$891$		0			0
$892$	14.7529	−	14.4896i	0.493963	−	0.485149i
$893$	−74.2053	+	13.0844i	−2.48318	+	0.437852i
$894$		0			0
$895$	−4.71438	−	12.9526i	−0.157584	−	0.432959i
$896$	13.9903	+	4.90074i	0.467382	+	0.163722i
$897$		0			0
$898$	8.39205	+	7.75967i	0.280046	+	0.258943i
$899$	7.19828	+	12.4678i	0.240076	+	0.415824i
$900$		0			0
$901$	9.33569	−	16.1699i	0.311017	−	0.538697i
$902$	14.5102	−	4.50335i	0.483137	−	0.149945i
$903$		0			0
$904$	9.72166	−	2.01792i	0.323338	−	0.0671152i
$905$	−35.8599	−	6.32307i	−1.19202	−	0.210186i
$906$		0			0
$907$	37.4764	+	44.6626i	1.24438	+	1.48300i	0.814553	+	0.580089i	$0.196982\pi$
$907$	37.4764	+	44.6626i	1.24438	+	1.48300i	0.429831	+	0.902909i	$0.358573\pi$
$908$	0.185983	−	0.0480439i	0.00617206	−	0.00159439i
$909$		0			0
$910$	−18.9772	+	2.41155i	−0.629088	+	0.0799422i
$911$	−3.70530	−	1.34862i	−0.122762	−	0.0446817i	0.279909	−	0.960027i	$-0.409696\pi$
$911$	−3.70530	−	1.34862i	−0.122762	−	0.0446817i	−0.402671	+	0.915345i	$0.631918\pi$
$912$		0			0
$913$	−19.7774	−	16.5952i	−0.654537	−	0.549222i
$914$	0.168355	−	3.49493i	0.00556870	−	0.115602i
$915$		0			0
$916$	31.2223	−	43.7467i	1.03162	−	1.44543i
$917$		−	6.72250i		−	0.221997i
$918$		0			0
$919$			6.45794i			0.213028i	0.994311	+	0.106514i	$0.0339689\pi$
$919$			6.45794i			0.213028i	−0.994311	+	0.106514i	$0.966031\pi$
$920$	−13.8661	+	8.57267i	−0.457151	+	0.282633i
$921$		0			0
$922$	−12.7634	−	0.614829i	−0.420340	−	0.0202483i
$923$	8.53374	+	7.16066i	0.280891	+	0.235696i
$924$		0			0
$925$	1.16842	+	0.425272i	0.0384175	+	0.0139828i
$926$	0.248631	+	1.95655i	0.00817054	+	0.0642963i
$927$		0			0
$928$	16.4591	+	22.4798i	0.540297	+	0.737936i
$929$	36.6277	+	43.6512i	1.20172	+	1.43215i	0.872998	+	0.487723i	$0.162172\pi$
$929$	36.6277	+	43.6512i	1.20172	+	1.43215i	0.328719	+	0.944428i	$0.393383\pi$
$930$		0			0
$931$	−32.7412	−	5.77316i	−1.07305	−	0.189208i
$932$	−8.19163	−	11.9259i	−0.268326	−	0.390647i
$933$		0			0
$934$	8.84417	+	28.4967i	0.289390	+	0.932441i
$935$	−14.9262	+	25.8530i	−0.488140	+	0.845483i
$936$		0			0
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	0.978965	−	0.204027i	$-0.0654031\pi$
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	−0.666175	+	0.745795i	$0.732070\pi$
$938$	−15.0133	+	16.2368i	−0.490201	+	0.530150i
$939$		0			0
$940$	54.2385	−	4.25365i	1.76906	−	0.138739i
$941$	6.39294	+	17.5645i	0.208404	+	0.572585i	0.999221	−	0.0394679i	$-0.0125663\pi$
$941$	6.39294	+	17.5645i	0.208404	+	0.572585i	−0.790817	+	0.612053i	$0.790344\pi$
$942$		0			0
$943$	−9.92488	+	1.75002i	−0.323198	+	0.0569886i
$944$	−0.825237	+	45.8329i	−0.0268592	+	1.49173i
$945$		0			0
$946$	−29.9991	−	12.5845i	−0.975354	−	0.409158i
$947$	−4.94182	−	28.0265i	−0.160588	−	0.910738i	−0.953498	−	0.301400i	$-0.902546\pi$
$947$	−4.94182	−	28.0265i	−0.160588	−	0.910738i	0.792910	−	0.609338i	$-0.208565\pi$
$948$		0			0
$949$	26.4054	−	9.61079i	0.857157	−	0.311980i
$950$	0.655996	+	1.27413i	0.0212833	+	0.0413381i
$951$		0			0
$952$	−17.9982	+	0.542463i	−0.583326	+	0.0175813i
$953$	−39.0891	+	22.5681i	−1.26622	+	0.731052i	−0.974270	−	0.225382i	$-0.927637\pi$
$953$	−39.0891	+	22.5681i	−1.26622	+	0.731052i	−0.291949	+	0.956434i	$0.594304\pi$
$954$		0			0
$955$	−23.0134	−	13.2868i	−0.744695	−	0.429950i
$956$	−25.3961	−	2.45242i	−0.821368	−	0.0793168i
$957$		0			0
$958$	−17.3691	−	11.1756i	−0.561171	−	0.361066i
$959$	−0.411444	+	2.33341i	−0.0132862	+	0.0753499i
$960$		0			0
$961$	17.2022	−	14.4343i	0.554909	−	0.465624i
$962$	30.0315	+	39.5047i	0.968253	+	1.27368i
$963$		0			0
$964$	4.05152	−	14.5937i	0.130491	−	0.470032i
$965$	−13.6530	+	37.5112i	−0.439504	+	1.20753i
$966$		0			0
$967$	−5.89240	+	7.02229i	−0.189487	+	0.225822i	−0.852421	−	0.522856i	$-0.824867\pi$
$967$	−5.89240	+	7.02229i	−0.189487	+	0.225822i	0.662934	+	0.748678i	$0.269311\pi$
$968$	−7.78045	+	6.93855i	−0.250073	+	0.223014i
$969$		0			0
$970$	−6.21200	+	27.4356i	−0.199455	+	0.880903i
$971$	−10.7197			−0.344010			−0.172005	−	0.985096i	$-0.555025\pi$
$971$	−10.7197			−0.344010			−0.172005	+	0.985096i	$0.555025\pi$
$972$		0			0
$973$	−17.0344			−0.546098
$974$	−0.0882385	+	0.389709i	−0.00282734	+	0.0124871i
$975$		0			0
$976$	−0.0511266	−	0.148748i	−0.00163652	−	0.00476131i
$977$	32.0082	−	38.1459i	1.02403	−	1.22040i	0.0488952	−	0.998804i	$-0.484430\pi$
$977$	32.0082	−	38.1459i	1.02403	−	1.22040i	0.975139	−	0.221593i	$-0.0711256\pi$
$978$		0			0
$979$	6.39836	−	17.5793i	0.204492	−	0.561838i
$980$	23.1300	+	6.42138i	0.738862	+	0.205123i
$981$		0			0
$982$	−13.2649	−	17.4492i	−0.423299	−	0.556826i
$983$	−1.39362	+	1.16939i	−0.0444496	+	0.0372976i	−0.664742	−	0.747073i	$-0.731458\pi$
$983$	−1.39362	+	1.16939i	−0.0444496	+	0.0372976i	0.620292	+	0.784371i	$0.287014\pi$
$984$		0			0
$985$	−9.09251	+	51.5662i	−0.289712	+	1.64304i
$986$	−28.4606	−	18.3120i	−0.906371	−	0.583174i
$987$		0			0
$988$	−5.49739	+	56.9285i	−0.174895	+	1.81114i
$989$	18.6883	+	10.7897i	0.594252	+	0.343092i
$990$		0			0
$991$	−48.8792	+	28.2204i	−1.55270	+	0.896451i	−0.554777	+	0.831999i	$0.687196\pi$
$991$	−48.8792	+	28.2204i	−1.55270	+	0.896451i	−0.997921	+	0.0644516i	$0.979470\pi$
$992$	−11.4425	+	11.9366i	−0.363300	+	0.378986i
$993$		0			0
$994$	2.07928	+	4.03853i	0.0659507	+	0.128094i
$995$	−6.67441	+	2.42928i	−0.211593	+	0.0770135i
$996$		0			0
$997$	2.04998	+	11.6260i	0.0649234	+	0.368199i	0.999909	+	0.0135125i	$0.00430130\pi$
$997$	2.04998	+	11.6260i	0.0649234	+	0.368199i	−0.934985	+	0.354687i	$0.884588\pi$
$998$	53.3333	+	22.3731i	1.68824	+	0.708209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.b.215.15		96
3.2	odd	2		972.2.l.c.215.2		96
4.3	odd	2	inner	972.2.l.b.215.13		96
9.2	odd	6		972.2.l.d.863.10		96
9.4	even	3		324.2.l.a.179.4		96
9.5	odd	6		108.2.l.a.23.13	yes	96
9.7	even	3		972.2.l.a.863.7		96
12.11	even	2		972.2.l.c.215.4		96
27.2	odd	18	inner	972.2.l.b.755.13		96
27.7	even	9		972.2.l.d.107.15		96
27.11	odd	18		324.2.l.a.143.9		96
27.16	even	9		108.2.l.a.47.8	yes	96
27.20	odd	18		972.2.l.a.107.2		96
27.25	even	9		972.2.l.c.755.4		96
36.7	odd	6		972.2.l.a.863.2		96
36.11	even	6		972.2.l.d.863.15		96
36.23	even	6		108.2.l.a.23.8	✓	96
36.31	odd	6		324.2.l.a.179.9		96
108.7	odd	18		972.2.l.d.107.10		96
108.11	even	18		324.2.l.a.143.4		96
108.43	odd	18		108.2.l.a.47.13	yes	96
108.47	even	18		972.2.l.a.107.7		96
108.79	odd	18		972.2.l.c.755.2		96
108.83	even	18	inner	972.2.l.b.755.15		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.8	✓	96	36.23	even	6
108.2.l.a.23.13	yes	96	9.5	odd	6
108.2.l.a.47.8	yes	96	27.16	even	9
108.2.l.a.47.13	yes	96	108.43	odd	18
324.2.l.a.143.4		96	108.11	even	18
324.2.l.a.143.9		96	27.11	odd	18
324.2.l.a.179.4		96	9.4	even	3
324.2.l.a.179.9		96	36.31	odd	6
972.2.l.a.107.2		96	27.20	odd	18
972.2.l.a.107.7		96	108.47	even	18
972.2.l.a.863.2		96	36.7	odd	6
972.2.l.a.863.7		96	9.7	even	3
972.2.l.b.215.13		96	4.3	odd	2	inner
972.2.l.b.215.15		96	1.1	even	1	trivial
972.2.l.b.755.13		96	27.2	odd	18	inner
972.2.l.b.755.15		96	108.83	even	18	inner
972.2.l.c.215.2		96	3.2	odd	2
972.2.l.c.215.4		96	12.11	even	2
972.2.l.c.755.2		96	108.79	odd	18
972.2.l.c.755.4		96	27.25	even	9
972.2.l.d.107.10		96	108.7	odd	18
972.2.l.d.107.15		96	27.7	even	9
972.2.l.d.863.10		96	9.2	odd	6
972.2.l.d.863.15		96	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37930 + 0.312303i) q^{2} +(1.80493 + 0.861519i) q^{4} +(1.46028 - 1.74029i) q^{5} +(0.448132 - 1.23123i) q^{7} +(2.22049 + 1.75198i) q^{8} +(2.55766 - 1.94434i) q^{10} +(2.07176 - 1.73841i) q^{11} +(0.789120 - 4.47532i) q^{13} +(1.00263 - 1.55829i) q^{14} +(2.51557 + 3.10997i) q^{16} +(-4.20783 - 2.42939i) q^{17} +(-5.44971 + 3.14639i) q^{19} +(4.13500 - 1.88306i) q^{20} +(3.40048 - 1.75077i) q^{22} +(-2.38405 + 0.867725i) q^{23} +(-0.0279630 - 0.158586i) q^{25} +(2.48609 - 5.92636i) q^{26} +(1.86958 - 1.83622i) q^{28} +(4.85038 - 0.855253i) q^{29} +(0.999738 + 2.74676i) q^{31} +(2.49847 + 5.07520i) q^{32} +(-5.04515 - 4.66498i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(-8.49941 + 2.63785i) q^{38} +(6.29149 - 1.30592i) q^{40} +(3.91196 + 0.689785i) q^{41} +(-5.46733 - 6.51571i) q^{43} +(5.23705 - 1.35286i) q^{44} +(-3.55932 + 0.452305i) q^{46} +(11.2519 + 4.09536i) q^{47} +(4.04720 + 3.39600i) q^{49} +(0.0109576 - 0.227471i) q^{50} +(5.27988 - 7.39781i) q^{52} +3.84281i q^{53} -6.14402i q^{55} +(3.15217 - 1.94882i) q^{56} +(6.95722 + 0.335138i) q^{58} +(8.77893 + 7.36639i) q^{59} +(-0.0369509 - 0.0134490i) q^{61} +(0.521117 + 4.10082i) q^{62} +(1.86114 + 7.78050i) q^{64} +(-6.63603 - 7.90851i) q^{65} +(-11.7530 - 2.07238i) q^{67} +(-5.50189 - 8.01001i) q^{68} +(-1.24776 - 4.02040i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-7.41349 + 8.01766i) q^{74} +(-12.5470 + 0.984001i) q^{76} +(-1.21197 - 3.32985i) q^{77} +(-5.93205 + 1.04598i) q^{79} +(9.08569 + 0.163591i) q^{80} +(5.18035 + 2.17314i) q^{82} +(-1.65768 - 9.40119i) q^{83} +(-10.3725 + 3.77526i) q^{85} +(-5.50621 - 10.6946i) q^{86} +(7.64596 - 0.230448i) q^{88} +(5.99050 - 3.45862i) q^{89} +(-5.15653 - 2.97713i) q^{91} +(-5.05062 - 0.487722i) q^{92} +(14.2408 + 9.16274i) q^{94} +(-2.48245 + 14.0787i) q^{95} +(-6.70720 + 5.62801i) q^{97} +(4.52172 + 5.94806i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 9 q^{8} - 3 q^{10} + 6 q^{13} + 12 q^{14} + 3 q^{16} + 18 q^{17} - 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 6 q^{29} + 57 q^{32} - 3 q^{34} - 6 q^{37} - 45 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 9 * q^8 - 3 * q^10 + 6 * q^13 + 12 * q^14 + 3 * q^16 + 18 * q^17 - 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 6 * q^29 + 57 * q^32 - 3 * q^34 - 6 * q^37 - 45 * q^38 - 12 * q^40 - 66 * q^41 - 63 * q^44 - 3 * q^46 + 6 * q^49 + 66 * q^50 - 24 * q^52 + 81 * q^56 - 24 * q^58 + 6 * q^61 - 90 * q^62 - 3 * q^64 + 42 * q^65 - 51 * q^68 - 30 * q^70 - 6 * q^73 + 96 * q^74 - 9 * q^76 - 30 * q^77 - 12 * q^82 + 66 * q^85 - 141 * q^86 - 45 * q^88 + 24 * q^92 - 51 * q^94 + 42 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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